Core foundations of early mathematics: refining the number sense framework

Preschool number sense can be operationalized as three interconnected strands — number, number relations, and number operations. These strands involve key ideas that are foundational to mathematics education. Recent cognitive and behavioral research refines and extends our understanding of the early number sense framework in the following ways: (1) Although number sense can be viewed as a single construct, each strand predicts achievement when controlling for the others, and the strands appear to reinforce each other during development; (2) Level of representation (i.e. nonsymbolic versus symbolic) and set size affect children's competencies and development within and across strands and should be considered in intervention research; (3) There are substantial individual differences in preschoolers’ number sense knowledge. We argue that instruction must weave together these number sense strands from the start of preschool to prepare children for success in formal mathematics.